Currencies are expressed as pairs, eg AUD/USD. However if I wanted to express the value of the (somewhat nonsensical) AUD alone (or changes in its value), how might we attempt/approximate this? I realise that this is an intractable problem and also is very much based on what objective function you seek. So, there is no one answer, and it's very much a crude subjective goal.

For example, I've seen the USD index calculated using this form:

https://www.thebalance.com/u-s-dollar-i ... ta-3306249

My thinking is this - imagine that hypothetically currencies did have absolute values. And that they were stochastic processes with correlation between them. Given a deep enough time series, we should be able to reverse this back from a covariance matrix.

Any thoughts would be appreciated. I do recognise the nonsensical problem with this question, so please take it as being fuzzy. I'm fishing for useful ideas, so that we could visually express say a chart of AUD without undue influence from the effect of other currencies.